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Simplifying 0 = x4 + -24x2 + -432 Reorder the terms: 0 = -432 + -24x2 + x4 Solving 0 = -432 + -24x2 + x4 Solving for variable 'x'. Combine like terms: 0 + 432 = 432 432 + 24x2 + -1x4 = -432 + -24x2 + x4 + 432 + 24x2 + -1x4 Reorder the terms: 432 + 24x2 + -1x4 = -432 + 432 + -24x2 + 24x2 + x4 + -1x4 Combine like terms: -432 + 432 = 0 432 + 24x2 + -1x4 = 0 + -24x2 + 24x2 + x4 + -1x4 432 + 24x2 + -1x4 = -24x2 + 24x2 + x4 + -1x4 Combine like terms: -24x2 + 24x2 = 0 432 + 24x2 + -1x4 = 0 + x4 + -1x4 432 + 24x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 432 + 24x2 + -1x4 = 0 Factor a trinomial. (36 + -1x2)(12 + x2) = 0 Factor a difference between two squares. ((6 + x)(6 + -1x))(12 + x2) = 0Subproblem 1
Set the factor '(12 + x2)' equal to zero and attempt to solve: Simplifying 12 + x2 = 0 Solving 12 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x2 = 0 + -12 x2 = 0 + -12 Combine like terms: 0 + -12 = -12 x2 = -12 Simplifying x2 = -12 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-6, 6}
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